The present invention relates to pulse width modulated (PWM) voltage conversion and more particularly to an apparatus and/or method for providing different modulating waveforms as a function of a modulation index to achieve linearity between the modulating waveforms and output voltages throughout an extended range of inverter operation with minimal switching losses, minimal harmonic distortion and so as to achieve high overall inverter gain.
Many motor applications require that a motor be driven at various speeds. Motor speed can be adjusted with an adjustable speed drive (ASD) which is placed between a voltage source and an associated motor which can excite the motor at various frequencies. One commonly used type of ASD employs a PWM inverter and associated PWM controller which can control both voltage and frequency of signals that eventually reach motor stator windings.
A typical PWM controller receives three modulating signals, each modulating signal 120 degrees out of phase with the other two modulating signals, and a triangle carrier signal, compares each modulating signal to the carrier signal and generates a plurality of firing signals corresponding to each modulating signal. When a modulating signal is greater than the carrier signal, a corresponding firing signal is high. When a modulating signal is less than the carrier signal, a corresponding firing signal is low.
The firing signals are used to control an associated PWM inverter A PWM inverter consists of a plurality of switches that alternately connect associated motor stator windings to positive and negative DC voltage buses to produce a series of high frequency positive and negative voltage pulses that excite the motor stator windings. By firing the PWM switches according to the firing signals, the widths of the positive pulses relative to the widths of the negative pulses over a series of high frequency pulses varies. The varying widths over a modulating signal period generate a low frequency alternating voltage. When the carrier signal has a high frequency and the maximum magnitude of the modulating signal is less than the magnitude of the DC bus voltage, the generated alternating voltage approximately linearly tracks the modulating signal. Thus, where a modulating signal is sinusoidal, the generated alternating phase voltage is sinusoidal and has a frequency equal to the frequency of the modulating signal.
The phase voltages result in line to line voltages which in turn cause line to line currents which lag the line to line voltages by a phase angle .PHI.. The generated line to line alternating currents drive the motor which operates at the alternating current frequency. Where the line to line voltages and currents are sinusoidal, the motor is driven smoothly. However, where harmonics occur in the line to line voltages imperfect and inefficient rotation occurs.
For the purposes of this explanation an amplitude modulation index Mi is defined as the ratio of a peak modulation signal value V.sub.mp to a function of DC bus voltage such that: EQU Mi=(V.sub.mp)/((2/.pi.)(V.sub.dc)) Eq. 1
By increasing the index M.sub.i, the amplitude of the generated alternating voltage can be increased. In addition, because the generated alternating voltage and associated current track the modulating signal, by changing the frequency of the modulating signal, the frequency of the generated alternating current, and thus the motor speed, can be altered. For example, by increasing the frequency of the modulating signal, the frequency of the alternating current can be increased and motor speed can in turn be increased. Motor speed can be decreased by decreasing the sinusoidal modulating signal frequency.
Several different modulating signal waveforms can be used by a controller to generate firing pulses which result in sinusoidal line to line voltages and line to line currents. Because the modulating signals are 120 degrees out of phase, where the modulating signals are sinusoidal, the line to line voltage across any two stator windings (i.e. between any two inverter outputs) will be sinusoidal. In addition, if precisely the same zero sequence signal is added to three sinusoidal modulating signals which are 120 degrees out of phase, resulting line to line voltages will still be sinusoidal.
Thus, waveform sets which can be used to generate sinusoidal line to line voltages and currents include a first set including three sinusoidal waveforms, one waveform for each inverter phase, each waveform 120 degrees out of phase with the other two waveforms and several other sets of waveforms wherein zero sequence signals are added to three sinusoidal waveforms, each of the three resulting waveforms corresponding to a separate one of the three inverter phases.
Modulating waveforms which generate sinusoidal line to line voltages and currents can generally be divided into two different types including continuous PWM (CPWM) and discontinuous PWM (DPWM) waveforms.
CPWM waveforms, on one hand, are waveforms which are generated with the intention that, during each modulating signal cycle switching occurs each carrier signal cycle. In other words, pulse width modulation is intended to be continuous throughout the modulating signal cycle, hence the term "continuous" PWM. As well known in the art one type of CPWM waveform is the simple sinusoid. In addition, other types of CPWM waveforms can be formed by adding specific zero sequence signals to simple sinusoids.
DPWM waveforms, on the other hand, are waveforms which, during some portion of the modulating signal cycle, are purposefully set equal to the peak carrier signal value so that switching does not occur during at least some carrier signal cycles. In other words, pulse width modulation is discontinuous during each modulating signal cycle, hence the term "discontinuous" PWM. With DPWM signals, during periods when switches in one phase are not switching, modulating signals corresponding to the other two phases are generated such that the resulting line to line voltages remain sinusoidal. DPWM waveforms consist of specific zero sequence signals added to simple sinusoids.
While theoretically an infinite number of zero sequence signals and therefrom CPWM and DPWM modulating signals could be generated, the performance and simplicity constraints of practical PWM-VSI drives reduce possible modulating signals to a small number. For the purposes of the present invention, in addition to SPWM signals, only two other types of CPWM modulating signals will be considered, third harmonic injection PWM (THIPWM) and space vector PWM (SVPWM). THIPWM modulating signals are formed by adding a zero sequence signal to each of three sinusoidal signals where the zero sequence signal is the third harmonic of one of the sinusoidal signals. SVPWM signals are formed by adding a zero sequence signal to each of three sinusoidal signals where the zero sequence signal has a frequency three times that of one of the sinusoidal signals and is a saw tooth signal.
In addition, only two DPWM modulating signals referred to herein as DPWM1 and DPWM2 will be explained.
DPWM1 signals are generated by adding a zero sequence signal to each of three sinusoidal modulating signals where the zero sequence signal has an instantaneous magnitude equal to the magnitude of the difference between a peak carrier signal value and the instantaneous maximum modulating signal magnitude and has the sign of the instantaneous maximum modulating signal. DPWM2 signals are generated by adding a zero sequence signal to each of three sinusoidal modulating signals where the zero sequence signals are generated by first phase shifting each of the three sinusoidal modulating signals 30.degree. to form shifted signals and then the zero sequence signal has an instantaneous magnitude equal to the magnitude of the difference between a peak carrier signal value and the instantaneous maximum shifted signal magnitude and has the sign of the instantaneous maximum shifted signal. The DPWM2 zero sequence signal is added to each of the original, non-shifted modulating sinusoidal signals to yield the DPWM2 modulating signals.
Clearly SPWM signals are the simplest to understand and to generate. In addition, SPWM generates relatively low harmonic distortion at low Mi values. However, while sinusoidal signals have some advantages, they suffer from at least two important shortcomings. First, where the modulating index Mi exceeds unity (i.e. the peak value of the modulating signal is greater than the peak value of the carrier signal), during extreme high and low portions of the modulating signal, the modulating signal and carrier signal do not intersect and switching is discontinued. During these times, because switching is discontinued, the PWM inverter cannot alter the low frequency alternating voltage to reflect variations in modulating signal amplitude. The inverter is said to be saturated and the relationship between the generated alternating voltage and the modulating signal becomes non-linear. The region of operation starting from the end of linear operation and continuing through the six-step operating point (i.e. where Mi=1.0) is commonly referred to as the overmodulation region. An SPWM linear modulation range ends at a modulating index Mi (as defined in Equation 1) of approximately 0.785.
Second, as PWM inverter switches are opened and closed, PWM inverter output is diminished by conduction and switching losses. These losses are directly related to the duration of switch conducting time and the number of times the modulating and carrier signals intersect respectively. Unfortunately, a sinusoidal modulating signal where the modulating signal does not cause overmodulation intersects the carrier signal the maximum number of times per cycle producing high switching losses.
With an SPWM signal set the linear region of operation can be extended by increasing the amplitude of the modulating signals to compensate for non-linearities. For example, assuming SPWM modulating signals which cause operation in the overmodulation region, if, at a specific operating point, generated alternating signals are 5% less than intended, the amplitudes of the SPWM signals can be increased until the generated alternating signals increase by 5%. This correction may require an increase in modulating signal amplitudes of 10 to 12% for example. Such corrections can be made up until the six-step operating point.
Unfortunately, while correction to eliminate non-linearities in the over modulating region is possible, such correction is often difficult to accurately implement. For example, some controller processors are only equipped to manipulate 8 or 16-bit words. In some cases linear operation up to the six step operating point may require extremely large modulating signal amplitude (i.e. 100 or more times greater than the carrier signal value). In these cases processor word handling limitations can adversely affect modulating signal resolution and therefore can affect control accuracy generally. This in turn can cause excessive harmonics at high Mi values where resolution is most distorted.
Other CPWM signals minimize at least some of the shortcomings of SPWM signals. For example, THIPWM signals extends the linear operating region to approximately Mi=0.88 and SVPWM signals extend the linear operating region to approximately Mi=0.9078. In addition, each of the THIPWM and SVPWM signals causes less harmonic distortion than SPWM signals at higher Mi values. Moreover, both THIPWM and SVPWM increase the maximum possible generated alternating voltage prior to saturation.
However, each of the THIPWM and SVPWM signals still causes relatively large switching losses as switching occurs each carrier signal cycle. In addition, while each of these signals can be corrected to compensate for non-linearity in the overmodulation region, such correction is difficult to implement due to hardware word processing constraints.
DPWM signals overcome many of the shortcomings associated with CPWM signals generally. For example, because switching is discontinuous during at least some portion of each modulating signal cycle, switching losses are minimized. In addition, one DPWM method (e.g. DPWM1) can be corrected to compensate for non-linearities at high Mi values without reducing resolution and thus extend the region of linear operation. This is because the highest modulation signal value required or possible for DPWM is the peak carrier signal value. Thus, even at the six step operating point, the modulation index Mi is always a relatively small number when DPWM signals are used. In this case, even an 8 or 16-bit hardware constraint does not reduce resolution. Furthermore, it is well known that at high modulation indexes DPWM signals cause less harmonic distortion than CPWM signals.
Among DPWM signals, different DPWM signals have unique advantages. For example, in addition to being related to the number of times a modulating signal and a carrier signal intersect, switching losses are also related to the instantaneous generated alternating current level when a switch switches (i.e. opens or closes), the bus voltage level, and the time required for a switch to occur such that: EQU Switching Losses=V.sub.dc .multidot.I.sub.l .multidot.T.sub.switch Eq. 2
where I.sub.l is the instantaneous generated alternating current and T.sub.switch is the switch time for a particular device. Thus, DPWM signals which are equal to the peak carrier signal value during periods when the generated alternating current is highest cause less switching losses and therefore cause less harmonic distortion than DPWM signals which are tied to the peak carrier signal value during some other period (e.g. during peak modulating signal periods).
Unfortunately, at low modulation index values Mi, DPWM signals generally cause greater harmonic distortion than CPWM signals. This is because, while DPWM signals are formed by adding a common mode zero sequence signal to balanced three phase modulating signals thus preserving the line to line sinusoidal voltages, the PWM controller modifies the modulating signals as a function of the zero sequence signals on a per carrier cycle basis to generate modified pulses. The modified pulses produce harmonic distortion.
Thus, it would be advantageous to have a method and/or apparatus for providing modulating signals to a PWM inverter that achieve linearity throughout an extended range of inverter operation between the modulating signals and output voltages with minimal switching losses, minimal harmonic distortion and so as to achieve high overall inverter gain.